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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 14 Dec 2017 14:59:26 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/14/t15132599863aip7eullplts0x.htm/, Retrieved Tue, 14 May 2024 22:07:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309507, Retrieved Tue, 14 May 2024 22:07:03 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

102

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [] [2017-12-14 13:59:26] [56f5077a8f154f9e9b9da6af553a0e28] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309507&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309507&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309507&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.415498	-5.8613	0
2	-0.129698	-1.8296	0.034402
3	0.179095	2.5265	0.00615
4	0.10768	1.519	0.065174
5	-0.131898	-1.8607	0.032134
6	0.009475	0.1337	0.446905
7	0.133996	1.8902	0.030089
8	-0.102721	-1.4491	0.074448
9	-0.045855	-0.6469	0.259231
10	0.030513	0.4304	0.333672
11	0.213295	3.0089	0.00148
12	-0.385869	-5.4434	0
13	0.039445	0.5564	0.289265
14	0.164022	2.3138	0.010849
15	-0.049353	-0.6962	0.243555
16	-0.170227	-2.4013	0.008627
17	0.112118	1.5816	0.057662
18	0.044119	0.6224	0.267206
19	-0.144533	-2.0389	0.021392
20	0.039715	0.5602	0.287971
21	0.060253	0.85	0.198182
22	-0.118914	-1.6775	0.047509
23	0.078004	1.1004	0.136248

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.415498 & -5.8613 & 0 \tabularnewline
2 & -0.129698 & -1.8296 & 0.034402 \tabularnewline
3 & 0.179095 & 2.5265 & 0.00615 \tabularnewline
4 & 0.10768 & 1.519 & 0.065174 \tabularnewline
5 & -0.131898 & -1.8607 & 0.032134 \tabularnewline
6 & 0.009475 & 0.1337 & 0.446905 \tabularnewline
7 & 0.133996 & 1.8902 & 0.030089 \tabularnewline
8 & -0.102721 & -1.4491 & 0.074448 \tabularnewline
9 & -0.045855 & -0.6469 & 0.259231 \tabularnewline
10 & 0.030513 & 0.4304 & 0.333672 \tabularnewline
11 & 0.213295 & 3.0089 & 0.00148 \tabularnewline
12 & -0.385869 & -5.4434 & 0 \tabularnewline
13 & 0.039445 & 0.5564 & 0.289265 \tabularnewline
14 & 0.164022 & 2.3138 & 0.010849 \tabularnewline
15 & -0.049353 & -0.6962 & 0.243555 \tabularnewline
16 & -0.170227 & -2.4013 & 0.008627 \tabularnewline
17 & 0.112118 & 1.5816 & 0.057662 \tabularnewline
18 & 0.044119 & 0.6224 & 0.267206 \tabularnewline
19 & -0.144533 & -2.0389 & 0.021392 \tabularnewline
20 & 0.039715 & 0.5602 & 0.287971 \tabularnewline
21 & 0.060253 & 0.85 & 0.198182 \tabularnewline
22 & -0.118914 & -1.6775 & 0.047509 \tabularnewline
23 & 0.078004 & 1.1004 & 0.136248 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309507&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]-0.415498[/C][C]-5.8613[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.129698[/C][C]-1.8296[/C][C]0.034402[/C][/ROW]
[ROW][C]3[/C][C]0.179095[/C][C]2.5265[/C][C]0.00615[/C][/ROW]
[ROW][C]4[/C][C]0.10768[/C][C]1.519[/C][C]0.065174[/C][/ROW]
[ROW][C]5[/C][C]-0.131898[/C][C]-1.8607[/C][C]0.032134[/C][/ROW]
[ROW][C]6[/C][C]0.009475[/C][C]0.1337[/C][C]0.446905[/C][/ROW]
[ROW][C]7[/C][C]0.133996[/C][C]1.8902[/C][C]0.030089[/C][/ROW]
[ROW][C]8[/C][C]-0.102721[/C][C]-1.4491[/C][C]0.074448[/C][/ROW]
[ROW][C]9[/C][C]-0.045855[/C][C]-0.6469[/C][C]0.259231[/C][/ROW]
[ROW][C]10[/C][C]0.030513[/C][C]0.4304[/C][C]0.333672[/C][/ROW]
[ROW][C]11[/C][C]0.213295[/C][C]3.0089[/C][C]0.00148[/C][/ROW]
[ROW][C]12[/C][C]-0.385869[/C][C]-5.4434[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.039445[/C][C]0.5564[/C][C]0.289265[/C][/ROW]
[ROW][C]14[/C][C]0.164022[/C][C]2.3138[/C][C]0.010849[/C][/ROW]
[ROW][C]15[/C][C]-0.049353[/C][C]-0.6962[/C][C]0.243555[/C][/ROW]
[ROW][C]16[/C][C]-0.170227[/C][C]-2.4013[/C][C]0.008627[/C][/ROW]
[ROW][C]17[/C][C]0.112118[/C][C]1.5816[/C][C]0.057662[/C][/ROW]
[ROW][C]18[/C][C]0.044119[/C][C]0.6224[/C][C]0.267206[/C][/ROW]
[ROW][C]19[/C][C]-0.144533[/C][C]-2.0389[/C][C]0.021392[/C][/ROW]
[ROW][C]20[/C][C]0.039715[/C][C]0.5602[/C][C]0.287971[/C][/ROW]
[ROW][C]21[/C][C]0.060253[/C][C]0.85[/C][C]0.198182[/C][/ROW]
[ROW][C]22[/C][C]-0.118914[/C][C]-1.6775[/C][C]0.047509[/C][/ROW]
[ROW][C]23[/C][C]0.078004[/C][C]1.1004[/C][C]0.136248[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309507&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309507&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.415498	-5.8613	0
2	-0.129698	-1.8296	0.034402
3	0.179095	2.5265	0.00615
4	0.10768	1.519	0.065174
5	-0.131898	-1.8607	0.032134
6	0.009475	0.1337	0.446905
7	0.133996	1.8902	0.030089
8	-0.102721	-1.4491	0.074448
9	-0.045855	-0.6469	0.259231
10	0.030513	0.4304	0.333672
11	0.213295	3.0089	0.00148
12	-0.385869	-5.4434	0
13	0.039445	0.5564	0.289265
14	0.164022	2.3138	0.010849
15	-0.049353	-0.6962	0.243555
16	-0.170227	-2.4013	0.008627
17	0.112118	1.5816	0.057662
18	0.044119	0.6224	0.267206
19	-0.144533	-2.0389	0.021392
20	0.039715	0.5602	0.287971
21	0.060253	0.85	0.198182
22	-0.118914	-1.6775	0.047509
23	0.078004	1.1004	0.136248

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.415498	-5.8613	0
2	-0.365422	-5.1549	0
3	-0.064611	-0.9114	0.181581
4	0.188433	2.6582	0.004248
5	0.106341	1.5001	0.067583
6	0.041405	0.5841	0.279912
7	0.107754	1.5201	0.065042
8	-0.01544	-0.2178	0.4139
9	-0.084662	-1.1943	0.11689
10	-0.128794	-1.8169	0.035371
11	0.210741	2.9729	0.001657
12	-0.198722	-2.8033	0.002779
13	-0.254313	-3.5875	0.00021
14	-0.149373	-2.1072	0.018178
15	0.026238	0.3701	0.355841
16	-0.008787	-0.124	0.450735
17	0.028438	0.4012	0.344363
18	0.041229	0.5816	0.280744
19	-0.001878	-0.0265	0.489448
20	-0.043255	-0.6102	0.271217
21	-0.034249	-0.4831	0.314763
22	-0.179244	-2.5285	0.006115
23	0.157028	2.2152	0.013942

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.415498 & -5.8613 & 0 \tabularnewline
2 & -0.365422 & -5.1549 & 0 \tabularnewline
3 & -0.064611 & -0.9114 & 0.181581 \tabularnewline
4 & 0.188433 & 2.6582 & 0.004248 \tabularnewline
5 & 0.106341 & 1.5001 & 0.067583 \tabularnewline
6 & 0.041405 & 0.5841 & 0.279912 \tabularnewline
7 & 0.107754 & 1.5201 & 0.065042 \tabularnewline
8 & -0.01544 & -0.2178 & 0.4139 \tabularnewline
9 & -0.084662 & -1.1943 & 0.11689 \tabularnewline
10 & -0.128794 & -1.8169 & 0.035371 \tabularnewline
11 & 0.210741 & 2.9729 & 0.001657 \tabularnewline
12 & -0.198722 & -2.8033 & 0.002779 \tabularnewline
13 & -0.254313 & -3.5875 & 0.00021 \tabularnewline
14 & -0.149373 & -2.1072 & 0.018178 \tabularnewline
15 & 0.026238 & 0.3701 & 0.355841 \tabularnewline
16 & -0.008787 & -0.124 & 0.450735 \tabularnewline
17 & 0.028438 & 0.4012 & 0.344363 \tabularnewline
18 & 0.041229 & 0.5816 & 0.280744 \tabularnewline
19 & -0.001878 & -0.0265 & 0.489448 \tabularnewline
20 & -0.043255 & -0.6102 & 0.271217 \tabularnewline
21 & -0.034249 & -0.4831 & 0.314763 \tabularnewline
22 & -0.179244 & -2.5285 & 0.006115 \tabularnewline
23 & 0.157028 & 2.2152 & 0.013942 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309507&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]-0.415498[/C][C]-5.8613[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.365422[/C][C]-5.1549[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.064611[/C][C]-0.9114[/C][C]0.181581[/C][/ROW]
[ROW][C]4[/C][C]0.188433[/C][C]2.6582[/C][C]0.004248[/C][/ROW]
[ROW][C]5[/C][C]0.106341[/C][C]1.5001[/C][C]0.067583[/C][/ROW]
[ROW][C]6[/C][C]0.041405[/C][C]0.5841[/C][C]0.279912[/C][/ROW]
[ROW][C]7[/C][C]0.107754[/C][C]1.5201[/C][C]0.065042[/C][/ROW]
[ROW][C]8[/C][C]-0.01544[/C][C]-0.2178[/C][C]0.4139[/C][/ROW]
[ROW][C]9[/C][C]-0.084662[/C][C]-1.1943[/C][C]0.11689[/C][/ROW]
[ROW][C]10[/C][C]-0.128794[/C][C]-1.8169[/C][C]0.035371[/C][/ROW]
[ROW][C]11[/C][C]0.210741[/C][C]2.9729[/C][C]0.001657[/C][/ROW]
[ROW][C]12[/C][C]-0.198722[/C][C]-2.8033[/C][C]0.002779[/C][/ROW]
[ROW][C]13[/C][C]-0.254313[/C][C]-3.5875[/C][C]0.00021[/C][/ROW]
[ROW][C]14[/C][C]-0.149373[/C][C]-2.1072[/C][C]0.018178[/C][/ROW]
[ROW][C]15[/C][C]0.026238[/C][C]0.3701[/C][C]0.355841[/C][/ROW]
[ROW][C]16[/C][C]-0.008787[/C][C]-0.124[/C][C]0.450735[/C][/ROW]
[ROW][C]17[/C][C]0.028438[/C][C]0.4012[/C][C]0.344363[/C][/ROW]
[ROW][C]18[/C][C]0.041229[/C][C]0.5816[/C][C]0.280744[/C][/ROW]
[ROW][C]19[/C][C]-0.001878[/C][C]-0.0265[/C][C]0.489448[/C][/ROW]
[ROW][C]20[/C][C]-0.043255[/C][C]-0.6102[/C][C]0.271217[/C][/ROW]
[ROW][C]21[/C][C]-0.034249[/C][C]-0.4831[/C][C]0.314763[/C][/ROW]
[ROW][C]22[/C][C]-0.179244[/C][C]-2.5285[/C][C]0.006115[/C][/ROW]
[ROW][C]23[/C][C]0.157028[/C][C]2.2152[/C][C]0.013942[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309507&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309507&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.415498	-5.8613	0
2	-0.365422	-5.1549	0
3	-0.064611	-0.9114	0.181581
4	0.188433	2.6582	0.004248
5	0.106341	1.5001	0.067583
6	0.041405	0.5841	0.279912
7	0.107754	1.5201	0.065042
8	-0.01544	-0.2178	0.4139
9	-0.084662	-1.1943	0.11689
10	-0.128794	-1.8169	0.035371
11	0.210741	2.9729	0.001657
12	-0.198722	-2.8033	0.002779
13	-0.254313	-3.5875	0.00021
14	-0.149373	-2.1072	0.018178
15	0.026238	0.3701	0.355841
16	-0.008787	-0.124	0.450735
17	0.028438	0.4012	0.344363
18	0.041229	0.5816	0.280744
19	-0.001878	-0.0265	0.489448
20	-0.043255	-0.6102	0.271217
21	-0.034249	-0.4831	0.314763
22	-0.179244	-2.5285	0.006115
23	0.157028	2.2152	0.013942

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

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Figure 3

PNG link

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Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
x <- na.omit(x)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,'ACF(k)',header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,'PACF(k)',header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code